Power Sum

Probability Level 5

Find $\displaystyle \sum_{\{a_{1}, \ldots, a_{k}\} \subseteq \{1, 2, 3, 4, 5\}} \frac{1}{a_{1} \cdots a_{k}}$ , where the sum is over all nonempty subsets of of the set $\{1, 2, 3, 4, 5\}$ .